The present invention relates to an article, such as a film or a fibrous web.
Polymers are used extensively to make a variety of products which include blown and cast films, extruded sheets, injection molded articles, foams, blow molded articles, extruded pipe, monofilaments, and nonwoven webs. Some of such polymers, such as polyolefins, are naturally hydrophobic, and for many uses this property is either a positive attribute or at least not a disadvantage.
There are a number of uses for polymers, however, where their hydrophobic nature either limits their usefulness or requires some effort to modify the surface characteristics of the articles made therefrom. By way of example, polyolefins, such as polyethylene and polypropylene, are used to manufacture polymeric fabrics which are employed in the construction of such disposable absorbent articles as diapers; incontinent care products; feminine care products, such as sanitary napkins and tampons; filter elements; wipes; surgical gowns and drapes; protective pads; wound dressings, such as bandages; and the like. Such polymeric fabrics often are nonwoven webs prepared by, for example, such processes as meltblowing, coforming, and spunbonding. Frequently, such polymeric fabrics need to be wettable by water. Wettability can be obtained by spraying or otherwise coating (i.e., surface treating or topically treating) the fabric with a surfactant solution during or after its formation, and then drying the web.
Some of the more common topically applied surfactants are nonionic surfactants, such as polyethoxylated octylphenols and condensation products of propylene oxide with propylene glycol, by way of illustration only. These surfactants are effective in rendering normally hydrophobic polymeric fabrics wettable. However, the surfactant is readily removed from the fabric, often after only a single exposure to an aqueous liquid.
Substantial efforts have been directed to increasing the durability of surfactants which are topically applied to a polymeric fabric. Such efforts include the following, by way of illustration:
(1) use of a composition which includes water, a primary surfactant, and a cosurfactant which is functional to wet the fabric with the composition and which provides for substantially uniform distribution of the primary surfactant onto the polymeric fabric;
(2) use of a surfactant, with or without a nonionic cosurfactant, which is the reaction product of an acid anhydride derivative, such as a substituted succinic anhydride, with a polyhydroxy compound, such as sorbitol, a polyethylene glycol, triethanolamine, a polyhydroxyamine, certain primary and secondary amines, and certain unsaturated aliphatic sulfo compounds;
(3) use of a surfactant, with or without a nonionic cosurfactant, which is the reaction product of certain unsaturated aliphatic sulfo compounds with the reaction product of an acid anhydride derivative, such as a substituted succinic anhydride, with a polyamine having at least one NH group capable of addition to a double bond;
(4) use of a surfactant mixture which includes an ester-acid, ester salt, or a mixture thereof, and an amidic-acid, amidic salt, or mixture thereof, with or without a nonionic cosurfactant; and
(5) use of a surfactant mixture which includes a sorbitol succinate surfactant, such as an ethoxylated amino sorbitol succinate salt or an alkenyl succinate anhydride ethoxylated fatty amine salt, and a cowetting aid which can be, for example, a silicone polyether or a primary or secondary alcohol having up to about 8 carbon atoms.
In addition to water wettability, many absorbent, i.e., porous, products are concerned with, at least to some degree, the rate at which the aqueous liquid penetrates the porous product. For example, when the porous product is a nonwoven web or other fibrous material, the liquid must penetrate between the fibers of the web. A porous substrate in which an aqueous liquid penetrates at a rapid rate will be more effective in absorbing large volumes of liquid delivered over a short period of time, and, as a consequence, more effective in preventing or minimizing leakage. Furthermore, a porous substrate which quickly absorbs liquid will allow other components of an absorbent product to more effectively move liquid away from the locus of liquid insult to the remainder of the absorbent product. Therefore, more of the absorbent product will be available for absorption of the liquid.
It is known that the rate of penetration of a liquid into a porous substrate is directly proportional to the surface tension of the liquid and the cosine of the contact angle that the liquid makes with the surface of the substrate (see, e.g., A. W. Adamson, Chapter XIII, xe2x80x9cWetting, Flotation, and Detergencyxe2x80x9d in xe2x80x9cPhysical Chemistry of Surfaces,xe2x80x9d Fifth Edition, John Wiley and Sons, New York, 1990, pp. 495-496). Lowering the surface tension of the liquid, therefore, has an adverse effect. On the rate of liquid penetration. That is, when the surface tension of the liquid is decreased, the driving force of liquid penetration also is decreased. The cosine of the contact angle, on the other hand, is at a maximum value of 1 when the contact angle is zero. As the contact angle increases, the cosine decreases, approaching zero as the contact angle approaches 90xc2x0.
The methods of making a polymeric substrate wettable as described above all involve reducing the surface tension of the liquid to a value which is approximately the same as or lower than the surface free energy of the substrate to be wetted by the liquid. Such methods also lower the contact angle. However, as already noted, lowering both the surface tension of the liquid and the contact angle is counterproductive with respect to the rate of liquid penetration. Thus, there is a need for materials which are wettable and exhibit a rapid uptake of liquid.
The present invention addresses some of the difficulties and problems discussed above by providing a wettable article which also has a rapid rate of liquid penetration. Wettability and rapid liquid penetration properties are achieved by minimizing the reduction in the surface tension of an aqueous liquid coming in contact with the article while maintaining a small contact angle that the liquid makes with the surface of the article.
Accordingly, the present invention provides a wettable article consisting of an article with a hydrophobic surface having a coating which includes a surface free energy modifier and a surface-active agent. The hydrophobic surface may be composed of a hydrophobic polymer. The surface free energy modifier has a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable article may be exposed, and desirably is present in an amount sufficient to substantially cover the surface of the article. The surface-active agent is present in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier.
The article may be, by way of example only, a film or a fibrous sheet. The fibrous sheet may be a woven or nonwoven web.
The hydrophobic polymer may be, by way of example, a polyolefin. Typical polyolefins are polyethylene and polypropylene. Also by way of example, the surface free energy modifier may be a protein and the surface-active agent may be a polyethoxylated alkylphenol.
The present invention also provides a method of preparing a wettable article. The method involves forming an article by melt extrusion, at least a portion of which is formed from a polymeric composition which includes a hydrophobic polymer and a surface-active agent adapted to migrate to a surface of the article; and coating the surface of the article with a surface free energy modifier.
By way of example, the surface free energy modifier may have a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable article may be exposed. As another example, the surface free energy modifier may be present in an amount sufficient to substantially cover the surface of the article.
The method may include the additional step of causing the surface-active agent to migrate to the surface of the article in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier.
The present invention further provides a method of preparing a wettable article which involves forming an article by melt extrusion, wherein the article has a hydrophobic surface; coating the surface of the article with a surface free energy modifier; and treating the coated article with a surface-active agent. For example, the surface free energy modifier may have a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable article may be exposed. As another example, the surface-active agent may be present in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier.
The wettable article of the present invention may be employed as a component of a disposable absorbent product. The disposable absorbent product may be, for example, a diaper, a feminine care product, or an incontinent product.
As used herein, the terms xe2x80x9carticlexe2x80x9d and xe2x80x9cproductxe2x80x9d are synonyms and are meant to include any article or product which is formed by a melt-extrusion process, regardless of the size or shape of the article. As a practical matter, the present disclosure is directed primarily to melt-extruded films, fibers, and nonwoven webs comprised of such fibers. Nevertheless, other articles or products are deemed to come within the spirit and scope of the present invention.
In those embodiments in which the article is a nonwoven web, such nonwoven web in general can be prepared by any of the means known to those having ordinary skill in the art. For example, the nonwoven web can be prepared by such processes as meltblowing, coforming, spunbonding, hydroentangling, carding, air-laying, and wet-forming.
The nonwoven web more typically will be a nonwoven web prepared by meltblowing, coforming, spunbonding, and the like. By way of illustration only, such processes are exemplified by the following references which are incorporated herein by reference:
(a) meltblowing references include, by way of example, U.S. Pat. Nos. 3,016,599 to R. W. Perry, Jr., U.S. Pat. No. 3,704,198 to J. S. Prentice, U.S. Pat. No. 3,755,527 to J. P. Keller et al., U.S. Pat. No. 3,849,241 to R. R. Butin et al., U.S. Pat. No. 3,978,185 to R. R. Butin et al., and U.S. Pat. No. 4,663,220 to T. J. Wisneski et al. See, also, V. A. Wente, xe2x80x9cSuperfine Thermoplastic Fibersxe2x80x9d, Industrial and Engineering Chemistry, Vol. 48, No. 8, pp. 1342-1346 (1956); V. A. Wente et al., xe2x80x9cManufacture of Superfine Organic Fibersxe2x80x9d, Navy Research Laboratory, Washington, D.C., NRL Report 4364 (111437), dated May 25, 1954, United States Department of Commerce, Office of Technical Services; and Robert R. Butin and Dwight T. Lohkamp, xe2x80x9cMelt Blowingxe2x80x94A One-Step Web Process for New Nonwoven Productsxe2x80x9d, Journal of the Technical Association of the Pulp and Paper Industry, Vol. 56, No.4, pp. 74-77 (1973);
(b) coforming references include U.S. Pat. No. 4,100,324 to R. A. Anderson et al. and U.S. Pat. No. 4,118,531 to E. R. Hauser; and
(c) spunbonding references include, among others, U.S. Pat. No. 3,341,394 to Kinney, U.S. Pat. No. 3,655,862 to Dorschner et al., U.S. Pat. No. 3,692,618 to Dorschner et al., U.S. Pat. No. 3,705,068 to Dobo et al., U.S. Pat. No. 3,802,817 to Matsuki et al., U.S. Pat. No. 3,853,651 to Porte, U.S. Pat. No. 4,064,605 to Akiyama et al., U.S. Pat. No. 4,091,140 to Harmon, U.S. Pat. No. 4,100,319 to Schwartz, U.S. Pat. No. 4,340,563 to Appel and Morman, U.S. Pat. No. 4,405,297 to Appel and Morman, U.S. Pat. No. 4,434,204 to Hartman et al., U.S. Pat. No. 4,627,811 to Greiser and Wagner, and U.S. Pat. No. 4,644,045 to Fowells.
The term xe2x80x9chydrophobic polymerxe2x80x9d is used herein to mean any polymer resistant to wetting, or not readily wet, by water, i.e., having a lack of affinity for water. A hydrophobic polymer typically will have a surface free energy of about 40 dynes/cm (40xc3x9710xe2x88x925 newtons/cm or N/cm) or less. Examples of hydrophobic polymers include, by way of illustration only, polyolefins, such as polyethylene, poly(isobutene), poly(isoprene), poly(4-methyl-1-pentene), polypropylene, ethylene-propylene copolymers, ethylene-propylene-hexadiene copolymers, and ethylene-vinyl acetate copolymers; styrene polymers, such as poly(styrene), poly(2-methylstyrene), styrene-acrylonitrile copolymers having less than about 20 mole-percent acrylonitrile, and styrene-2,2,3,3,-tetrafluoropropyl methacrylate copolymers; halogenated hydrocarbon polymers, such as poly(chlorotrifluoroethylene), chlorotrifluoroethylene-tetrafluoroethylene copolymers, poly(hexafluoropropylene), poly(tetrafluoroethylene), tetrafluoroethylene-ethylene copolymers, poly(trifluoroethylene), poly(vinyl fluoride), and poly(vinylidene fluoride); vinyl polymers, such as poly(vinyl butyrate), poly(vinyl decanoate), poly(vinyl dodecanoate), poly(vinyl hexadecanoate), poly(vinyl hexanoate), poly(vinyl propionate), poly(vinyl octanoate), poly(heptafluoroisopro-poxyethylene), 1-heptafluoroisopropoxymethylethylene-maleic acid copolymers, poly(heptafluoroisopropoxypropylene), poly(methacrylonitrile), poly(vinyl alcohol), poly(vinyl butyral), poly(ethoxyethylene), poly(methoxyethylene), and poly(vinyl formal); acrylic polymers, such as poly(n-butyl acetate), poly(ethyl acrylate), poly[(1-chlorodifluoromethyl)-tetrafluoroethyl acrylate], poly[di(chlorofluoromethyl)fluoro-methyl acrylate], poly(1,1-dihydroheptafluorobutyl acrylate), poly(1,1-dihydropentafluoroisopropyl acrylate), poly(1,1-dihydropentadecafluorooctyl acrylate), poly(heptafluoroiso-propyl acrylate), poly[5-(heptafluoroiospropoxy)pentyl acrylate], poly[11-(heptafluoroiospropoxy)undecyl acrylate], poly[2-(heptafluoropropoxy)ethyl acrylate], and poly(nona-fluoroisobutyl acrylate); methacrylic polymers, such as poly(benzyl methacrylate), poly(n-butyl methacrylate), poly(isobutyl methacrylate), poly(t-butyl methacrylate), poly(t-butylaminoethyl methacrylate), poly(dodecyl methacrylate), poly(ethyl methacrylate), poly(2-ethylhexyl methacrylate), poly(n-hexyl methacrylate), poly(dimethylaminoethyl methacrylate), poly(hydroxyethyl methacrylate), poly(phenyl methacrylate), poly(n-propyl methacrylate), poly(octadecyl methacrylate), poly(1,1-dihydropentadecafluorooctyl methacrylate), poly(heptafluoroisopropyl methacrylate), poly(heptadecafluorooctyl methacrylate), poly(1-hydrotetrafluoroethyl methacrylate), poly(1,1-dihydrotetrafluoropropyl methacrylate), poly(1-hydrohexafluoroisopropyl methacrylate), and poly(t-nonafluorobutyl methacrylate); polyethers, such as poly(chloral), poly(oxybutene)diol, poly(oxyisobutene)diol, poly(oxydecamethylene), poly(oxyethylene)-dimethyl ether polymers having molecular weights below about 1,500, poly(oxyhexamethylene)diol, poly(oxypropylene)diol, poly(oxypropylene)-dimethyl ether, and poly(oxytetramethylene); polyether copolymers, such as poly(oxyethylene)-poly(oxypropylene)-poly(oxyethylene) block copolymers, oxyethylene-oxypropylene copolymers having greater than about 20 mole percent oxypropylene, oxytetramethylene-oxypropylene copolymers, and block copolymers having oxyethylene-oxypropylene copolymer blocks separated by a poly(oxydimethylsilylene) block; polyamides, such as poly[imino(1-oxodecamethylene)], poly-[imino(1-oxododecamethylene)] or nylon 12, poly[imino(1-oxohexamethylene)] or nylon 6, poly[imino(1-oxotetramethylene)] or nylon 4, poly(iminoazelaoyliminononamethylene), poly(iminosebacoyliminodecamethylene), and poly(iminosuberoyliminooctamethylene); polyimines, such as poly[(benzoylimino)-ethylene], poly[(butyrylimino)ethylene], poly[(dodecanoylimino)ethylene], (dodecanoylimino)ethylene-(acetylimino)tri-methylene copolymers, poly[(heptanoylimino)ethylene], poly[(hexanoylimino)ethylene], poly{[(3-methyl)butyrylimino]-ethylene}, poly[(pentadecafluorooctadecanoylimino) ethylene], and poly[(pentanoylimino)ethylene]; polyurethanes, such as those prepared from methylenediphenyl diisocyanate and butanediol poly(oxytetramethylene)diol, hexamethylene diisocyanate and triethylene glycol, and 4-methyl-1,3-phenylene diisocyanate and tripropylene glycol; polysiloxanes, such as poly(oxydimethylsilylene) and poly(oxymethylphenylsilylene); and cellulosics, such as amylose, amylopectin, cellulose acetate butyrate, ethyl cellulose, hemicellulose, nitrocellulose, and starch.
As stated earlier, the wettable article of the present invention includes an article having a surface composed of a hydrophobic polymer. Thus, the term xe2x80x9csurfacexe2x80x9d is used herein to mean that portion of the total surface area of the article which is composed of a hydrophobic polymer. The surface of the article may encompass the entire surface area of the article or only a portion thereof. For example, when the article is a nonwoven web, the fibers of which the web is composed may be prepared from a single hydrophobic polymer. Alternatively, such fibers may be bicomponent fibers, in which one component is a hydrophobic polymer and the other component is a different hydrophobic polymer or a nonhydrophobic polymer, e.g., a hydrophilic polymer. The fibers may be sheath-core bicomponent fibers, in which case the sheath typically would be composed of a hydrophobic polymer. The fibers also may be side-by-side bicomponent fibers. Moreover, the fibers of which the nonwoven web is composed may have a circular or a noncircular cross-section. The fibers also may be polycomponent fibers, provided at least one component is a hydrophobic polymer.
The surface of the article of the present invention has a coating thereon. The coating includes a surface free energy modifier and a surface-active agent. The surface free energy modifier has a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable coated article may be exposed, and is present in an amount sufficient to substantially cover the surface of the article. That is, the surface of the article is covered with the surface free energy modifier to an extent such that the surface free energy of the portion of the article upon which the liquid impinges is the surface free energy of the surface free energy modifier, rather than the surface free energy of the hydrophobic polymer.
The surface free energy modifier may be any material which has a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable coated article may be exposed. Desirably, the surface free energy modifier will not be removed readily by the liquid environment. For example, when the hydrophobic polymer of which the surface is composed is a polyolefin, such as polypropylene, the surface free energy modifier may be a protein. The protein desirably will have a weight average molecular weight of at least about 10,000 Daltons. Examples of such proteins include, by way of illustration only, fibrinogen, such as baboon plasma fibrinogen, bovine plasma fibrinogen; cat plasma fibrinogen, dog plasma fibrinogen, goat plasma fibrinogen, guinea pig plasma fibrinogen, horse plasma fibrinogen, human plasma fibrinogen, mouse plasma fibrinogen, pig plasma fibrinogen, rabbit plasma fibrinogen, rat plasma fibrinogen, and sheep plasma fibrinogen; albumin, such as baboon albumin, bovine albumin, cat albumin, chicken albumin, chicken egg albumin, dog albumin, goat albumin, guinea pig albumin, hamster albumin, horse albumin, human albumin, mouse albumin, pig albumin, rabbit albumin, rat albumin, rhesus monkey albumin, sheep albumin, turkey albumin, and turkey egg albumin; casein, such as bovine milk casein, goat milk casein, human milk casein, sheep milk casein, and xcex1-, xcex2- and kappa-casein from bovine milk; hemoglobin, such as baboon hemoglobin, bovine hemoglobin, cat hemoglobin, dog hemoglobin, garter snake hemoglobin, goat hemoglobin, horse hemoglobin, human hemoglobin, mouse hemoglobin, pig hemoglobin, pigeon hemoglobin, rabbit hemoglobin, rat hemoglobin, sheep hemoglobin, and tukey hemoglobin; and lysozyme, such as chicken egg white lysozyme, human milk lysozyme, and turkey egg white lysozyme.
The surface of the article may be coated with the surface free energy modifier by any known means. For example, the surface free energy modifier may be simply adsorbed onto the surface of the article. As another example, the surface free energy modifier may be covalently bonded to the surface. As still another example, the surface of the article may be modified to assist or enhance either adsorption or covalent bonding. Thus, the surface may be exposed to a corona or plasma field or to electron beam or other ionizing radiation to aid either the adsorption or covalent bonding of the surface free energy modifier to the surface of the article; see, for example, U.S. Pat. No. 4,238,291 to Lowther, U.S. Pat. No. 3,754,117 to Walter, and U.S. Pat. No. 5,102,738 to Bell et al., each of which is incorporated herein by reference.
The term xe2x80x9csurface-active agentxe2x80x9d is used herein with its usual meaning and includes a single surface-active agent or a mixture of two or more surface-active agents. If a mixture of two or more surface-active agents is employed, the agents may be selected from the same or different classes, provided only that the agents present in the mixture are compatible with each other.
In general, the surface-active agent is present in the coating in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier.
The surface-active agent may be any surface active agent known to those having ordinary skill in the art, including anionic, cationic, and nonionic surfactants. Examples of anionic surfactants include, among others, linear and branched-chain sodium alkylbenzenesulfonates, linear and branched-chain alkyl sulfates, and linear and branched-chain alkyl ethoxy sulfates. Cationic surfactants include, by way of illustration, tallow trimethylammonium chloride. Examples of nonionic surfactants, include, again by way of illustration only, alkyl polyethoxylates; polyethoxylated alkylphenols; fatty acid ethanol amides; polysiloxane polyethers; and complex polymers of ethylene oxide, propylene oxide, and alcohols. Desirably, the surfactant will be a nonionic surfactant.
One method of the present invention for preparing a wettable article involves forming an article by melt extrusion, at least a portion of which is formed from a polymeric composition which includes a hydrophobic polymer and a surface-active agent adapted to migrate to the surface of the article. The presence of surface-active agent on the surface of the article immediately after its formation is acceptable, provided that (a) such presence does not significantly adversely interfere with the coating of the surface with a surface free energy modifier, described hereinafter, and (b) the coating of the surface with a surface free energy modifier results in a wettable article as defined herein. Desirably, migration of the surface-active agent takes place only after a migration-inducing, post-formation event, as described hereinafter.
The amount of surface-active agent included in the hydrophobic polymer may vary over a wide range. For example, the surface-active agent may be present in an amount of from about 0.01 to about 3 percent by weight, based on the hydrophobic polymer. As a further example, the surface-active agent may be present in an amount of from about 0.01 to about 1 percent by weight, based on the hydrophobic polymer. As still another example, when the surface-active agent is a polyethoxylated alkylphenol, the surface-active agent typically will be present in an amount of from about 0.05 to about 0.4 percent by weight, based on the hydrophobic polymer. Notwithstanding the foregoing ranges, the use of any amount of surface-active agent which results in a wettable surface is deemed to come within the scope of the present invention, provided that (a) the surface-active agent present on the surface does not significantly adversely interfere with the coating of the surface with a surface free energy modifier or (b) an amount of surface-active agent remains in the hydrophobic polymer which may be induced to migrate to the surface as described herein. If the presence of surface-active agent on the surface significantly interferes with the coating of the surface with a surface free energy modifier, the agent may be removed by, for example, washing the article with water before a coating procedure is carried out.
As noted above, the surface of the article is coated with a surface free energy modifier having a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable coated article may be exposed, in an amount sufficient to substantially cover the surface of the article. The coating may be applied by means which are well known to those having ordinary skill in the art, depending upon the nature of the modifier. For example, the surface may be coated with a protein by a simple topical treatment, such as dipping, spraying, brushing, direct and offset gravure printing, and doctor blading.
In the event the coating step removes the surface-active agent from the surface of the article, or the wettable article of the present invention does not result from the coating step, an additional step may be employed. The additional step involves causing the surface-active agent by a migration-inducing, post-formation event to migrate to the surface of the article in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier. An example of such a post-formation event is the coating of the surface with the surface free energy modifier, e.g., a protein. However, the migration of the surface-active agent after coating the surface is not rapid, and may require days or even weeks or months at ambient temperature (i.e., 20xc2x0-25xc2x0 C.). The migration may be expedited by heating the coated article at a temperature up to the temperature at which either the surface free energy modifier or the article begins to degrade. The time the coated article is heated depends on the temperature, with heating time being inversely proportional to the heating temperature. For example, the coated article may be heated at a temperature of from about 50xc2x0 C. to about 100xc2x0 C. for from about 30 minutes to about 10 hours.
Another method of the present invention for preparing a wettable article involves forming an article by melt extrusion, in which the article has a surface consisting of a hydrophobic polymer. The surface of the article is coated with a surface free energy modifier having a surface free energy greater than that of the surface of the article, but less than the surface tension of an aqueous liquid to which the wettable coated article may be exposed, in an amount sufficient to substantially cover the surface of the article. The coated article then is treated with a surface-active agent in an amount effective to lower the surface tension of the liquid to a value which is greater than the surface free energy of the surface of the article and equal to or less than the surface free energy of the surface free energy modifier.